At first sight, it seems to me that ω could be replaced by 0 in these formulas.For example : - [0] Next 0 = Fix (a -> Next^a 0) 0 = limit of 1, Next 0 = ε_0, Next^ε_0 0 = ε_ε_0, ... = ζ_0 - [0] Next ω = Fix (a -> Next^a 0) ω = limit of ω+1, Next^(ω+1) 0 = ε_(ω+1), Next^(ε_(ω+1)) 0 = ε_ε_(ω+1), ... = ζ_0Do you agree with this ?Have you an idea about the reason for which Simmons chose to use ω instead of 0 in his formulas ?

Do you know if there are standard forms, fundamental sequences and a comparison algorithm for this notation ?For the fundamental sequences I have an idea : perhaps we could take z+1, f(z+1), f(f(z+1)), ... as a fundamental sequence for Fix f z, is this correct?